| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 12.0.59182215273.1 |
$x^{12} - 5 x^{11} + 14 x^{10} - 31 x^{9} + 53 x^{8} - 72 x^{7} + 81 x^{6} - 72 x^{5} + 53 x^{4} - 31 x^{3} + 14 x^{2} - 5 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 433^{3}$ |
$2$ |
$7.90100981774$ |
$36.0416425818802$ |
|
|
✓ |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$6$ |
$5$ |
$4.35580546019$ |
| 12.0.126759838761.1 |
$x^{12} - 3 x^{11} + 6 x^{10} - 11 x^{9} + 15 x^{8} - 18 x^{7} + 21 x^{6} - 18 x^{5} + 15 x^{4} - 11 x^{3} + 6 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$3^{13}\cdot 43^{3}$ |
$2$ |
$8.4187666731$ |
$24.357295210976567$ |
|
|
✓ |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$6$ |
$5$ |
$8.68701246184$ |
| 12.0.218711265625.1 |
$x^{12} - 3 x^{11} + 8 x^{10} - 17 x^{9} + 29 x^{8} - 40 x^{7} + 45 x^{6} - 40 x^{5} + 29 x^{4} - 17 x^{3} + 8 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$5^{6}\cdot 241^{3}$ |
$2$ |
$8.81027090851$ |
$34.713109915419565$ |
|
|
✓ |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$3.17188678295$ |
| 12.0.239251750912.1 |
$x^{12} - 2 x^{11} + 5 x^{10} - 8 x^{9} + 11 x^{8} - 14 x^{7} + 15 x^{6} - 14 x^{5} + 11 x^{4} - 8 x^{3} + 5 x^{2} - 2 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 97^{3}$ |
$2$ |
$8.87642171229$ |
$27.85677655436824$ |
|
|
✓ |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$3.56895043616$ |
| 12.6.3495224609375.1 |
$x^{12} - x^{11} - 4 x^{10} + 5 x^{9} - 5 x^{8} + 14 x^{7} - 19 x^{6} + 14 x^{5} - 5 x^{4} + 5 x^{3} - 4 x^{2} - x + 1$ |
$12$ |
[6,3] |
$-\,5^{10}\cdot 71^{3}$ |
$2$ |
$11.0991466793$ |
$32.21841549588632$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$36.6945439221$ |
| 12.0.5156831600217.1 |
$x^{12} - x^{11} - 2 x^{10} + 4 x^{9} + 6 x^{8} - 27 x^{7} + 41 x^{6} - 27 x^{5} + 6 x^{4} + 4 x^{3} - 2 x^{2} - x + 1$ |
$12$ |
[0,6] |
$3^{7}\cdot 11^{9}$ |
$2$ |
$11.4647673394$ |
$21.761357200260658$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$30.4768591544$ |
| 12.6.6815156734375.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 11 x^{9} - 6 x^{8} - 21 x^{7} + 19 x^{6} + 12 x^{5} - 19 x^{4} + 2 x^{3} + 8 x^{2} - x - 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 11^{4}\cdot 31^{3}$ |
$3$ |
$11.7342765866$ |
$61.57829207131912$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$54.8065567524$ |
| 12.0.11209998860288.1 |
$x^{12} - 6 x^{10} - 4 x^{9} + 11 x^{8} + 8 x^{7} - 6 x^{6} + 8 x^{5} + 14 x^{4} + 8 x^{3} + 16 x^{2} + 16 x + 8$ |
$12$ |
[0,6] |
$2^{27}\cdot 17^{4}$ |
$2$ |
$12.2311454491$ |
$44.47661932088469$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$4$ |
$5$ |
$292.637308259$ |
| 12.0.18786186952704.1 |
$x^{12} - 4 x^{11} + 10 x^{10} - 12 x^{9} + x^{8} + 24 x^{7} - 32 x^{6} - 8 x^{5} + 90 x^{4} - 144 x^{3} + 128 x^{2} - 64 x + 16$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{7}$ |
$2$ |
$12.7688921852$ |
$24.23672593327708$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$254.776827382$ |
| 12.0.42845606719488.1 |
$x^{12} - 2 x^{9} + 6 x^{6} - 2 x^{3} + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{21}$ |
$2$ |
$13.6770423417$ |
$27.896364403879762$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$6$ |
$5$ |
$409.356139296$ |
| 12.0.104513734180864.1 |
$x^{12} + 4 x^{10} + 4 x^{8} - 12 x^{6} - 27 x^{4} + 48 x^{2} + 46$ |
$12$ |
[0,6] |
$2^{33}\cdot 23^{3}$ |
$2$ |
$14.7320928405$ |
$38.36665218650175$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[2]$ |
$2$ |
$5$ |
$245.00757893$ |
| 12.0.107567821094912.2 |
$x^{12} - 6 x^{11} + 21 x^{10} - 40 x^{9} + 67 x^{8} - 82 x^{7} + 95 x^{6} - 82 x^{5} + 67 x^{4} - 40 x^{3} + 21 x^{2} - 6 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 17^{7}$ |
$2$ |
$14.7674960818$ |
$29.98603852645895$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$107.753143277$ |
| 12.0.125765232361472.7 |
$x^{12} - 4 x^{10} + 2 x^{8} + 4 x^{6} + 9 x^{4} - 16 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{33}\cdot 11^{4}$ |
$2$ |
$14.961095086$ |
$39.56869954598961$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$652.032114089$ |
| 12.0.190210142896128.1 |
$x^{12} - 4 x^{9} + 10 x^{8} - 4 x^{7} + 8 x^{6} - 12 x^{5} + 3 x^{4} - 36 x^{3} + 12 x^{2} + 24 x + 6$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{11}$ |
$2$ |
$15.4858889046$ |
$50.414421537552215$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$1090.99835953$ |
| 12.0.213986410758144.1 |
$x^{12} + 6 x^{10} + 12 x^{8} + 24 x^{6} + 21 x^{4} - 6 x^{2} + 6$ |
$12$ |
[0,6] |
$2^{27}\cdot 3^{13}$ |
$2$ |
$15.6386352172$ |
$24.987759659239007$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[2]$ |
$2$ |
$5$ |
$476.442599046$ |
| 12.0.641959232274432.3 |
$x^{12} - 6 x^{10} + 12 x^{8} - 12 x^{6} + 45 x^{4} - 54 x^{2} + 18$ |
$12$ |
[0,6] |
$2^{27}\cdot 3^{14}$ |
$2$ |
$17.1379532612$ |
$30.93861708477606$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[2]$ |
$4$ |
$5$ |
$1628.85858364$ |
| 12.6.717439927058432.1 |
$x^{12} - 4 x^{10} - 12 x^{8} + 28 x^{6} - 59 x^{4} + 32 x^{2} - 2$ |
$12$ |
[6,3] |
$-\,2^{33}\cdot 17^{4}$ |
$2$ |
$17.2974517775$ |
$52.89191214766356$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$3868.05741211$ |
| 12.0.884272562962432.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 24 x^{9} + 60 x^{8} - 96 x^{7} + 176 x^{6} - 312 x^{5} + 325 x^{4} - 252 x^{3} + 328 x^{2} - 352 x + 146$ |
$12$ |
[0,6] |
$2^{30}\cdot 7^{7}$ |
$2$ |
$17.6014661934$ |
$34.04715710793443$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[2]$ |
$2$ |
$5$ |
$1205.94040784$ |
| 12.12.913378856890625.1 |
$x^{12} - x^{11} - 18 x^{10} + 8 x^{9} + 95 x^{8} - 14 x^{7} - 165 x^{6} + 23 x^{5} + 110 x^{4} - 17 x^{3} - 24 x^{2} + 2 x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 3881^{3}$ |
$2$ |
$17.6490329067$ |
$139.30183056945089$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$11$ |
$2191.75630691$ |
| 12.0.971471884263424.1 |
$x^{12} - 3 x^{11} + 11 x^{10} - 26 x^{9} + 65 x^{8} - 103 x^{7} + 126 x^{6} - 103 x^{5} + 65 x^{4} - 26 x^{3} + 11 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$2^{13}\cdot 17^{9}$ |
$2$ |
$17.7399552379$ |
$29.834929532638093$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[2]$ |
$2$ |
$5$ |
$991.013105733$ |
| 12.6.991623123042304.1 |
$x^{12} + 2 x^{10} - 29 x^{8} + 88 x^{6} - 128 x^{4} + 72 x^{2} - 4$ |
$12$ |
[6,3] |
$-\,2^{30}\cdot 31^{4}$ |
$2$ |
$17.7703324928$ |
$66.38555910891195$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$4672.44842236$ |
| 12.0.1032188877029888.1 |
$x^{12} - 5 x^{11} + 16 x^{10} - 42 x^{9} + 80 x^{8} - 82 x^{7} + 14 x^{6} + 29 x^{5} + 39 x^{4} - 104 x^{3} + 16 x^{2} + 48 x + 16$ |
$12$ |
[0,6] |
$2^{9}\cdot 17^{10}$ |
$2$ |
$17.8298051832$ |
$29.98603852645895$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$2385.44100064$ |
| 12.12.1356520905953125.1 |
$x^{12} - x^{11} - 16 x^{10} + 20 x^{9} + 60 x^{8} - 69 x^{7} - 79 x^{6} + 88 x^{5} + 35 x^{4} - 45 x^{3} - x^{2} + 7 x - 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 11^{4}\cdot 181^{3}$ |
$3$ |
$18.2404496882$ |
$148.79422637191786$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$11$ |
$2887.78342518$ |
| 12.0.1521681143169024.2 |
$x^{12} - 4 x^{11} + 2 x^{10} + 12 x^{9} - 23 x^{8} - 8 x^{7} + 104 x^{6} - 192 x^{5} + 210 x^{4} - 160 x^{3} + 88 x^{2} - 32 x + 8$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{11}$ |
$2$ |
$18.4159292675$ |
$34.955407562927284$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$5596.76379163$ |
| 12.0.1711891286065152.5 |
$x^{12} + 6 x^{10} + 15 x^{8} + 24 x^{6} + 24 x^{4} + 24 x^{2} + 12$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{13}$ |
$2$ |
$18.5975762693$ |
$24.987759659239007$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[2]$ |
$2$ |
$5$ |
$1638.66644501$ |
| 12.0.1721085137518592.3 |
$x^{12} - 6 x^{11} + 29 x^{10} - 90 x^{9} + 242 x^{8} - 494 x^{7} + 893 x^{6} - 1262 x^{5} + 1594 x^{4} - 1514 x^{3} + 1309 x^{2} - 702 x + 387$ |
$12$ |
[0,6] |
$2^{22}\cdot 17^{7}$ |
$2$ |
$18.6058791677$ |
$37.780041142444276$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$554.099176051$ |
| 12.6.2742118830047232.1 |
$x^{12} - 12 x^{10} + 54 x^{8} - 108 x^{6} + 81 x^{4} - 12$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 3^{21}$ |
$2$ |
$19.3422587728$ |
$27.896364403879762$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$10955.5789819$ |
| 12.0.2742118830047232.1 |
$x^{12} - 4 x^{9} + 54 x^{6} - 4 x^{3} + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{21}$ |
$2$ |
$19.3422587728$ |
$39.4514168808688$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$6$ |
$5$ |
$5033.99597721$ |
| 12.6.5135673858195456.1 |
$x^{12} - 6 x^{10} - 4 x^{9} + 3 x^{8} + 36 x^{7} - 4 x^{6} - 48 x^{5} - 6 x^{4} + 16 x^{3} + 24 x^{2} - 8$ |
$12$ |
[6,3] |
$-\,2^{30}\cdot 3^{14}$ |
$2$ |
$20.3805759548$ |
$30.93861708477606$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$12561.6080377$ |
| 12.0.5777633090469888.24 |
$x^{12} - 12 x^{10} - 8 x^{9} + 36 x^{8} + 60 x^{7} + 30 x^{6} - 3 x^{4} - 156 x^{3} - 54 x^{2} + 72 x + 50$ |
$12$ |
[0,6] |
$2^{27}\cdot 3^{16}$ |
$2$ |
$20.5816014074$ |
$47.429446013156884$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$4$ |
$5$ |
$21190.8408502$ |
| 12.6.11277990709674579.1 |
$x^{12} - 12 x^{10} + 54 x^{8} - 97 x^{6} + 15 x^{4} + 99 x^{2} - 44$ |
$12$ |
[6,3] |
$-\,3^{14}\cdot 11^{9}$ |
$2$ |
$21.7613572003$ |
$21.761357200260658$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$7858.52965367$ |
| 12.6.14280872991653888.1 |
$x^{12} - 2 x^{11} - 11 x^{10} + 14 x^{9} + 80 x^{8} - 218 x^{7} + 131 x^{6} + 218 x^{5} - 324 x^{4} + 82 x^{3} + 141 x^{2} - 46 x - 17$ |
$12$ |
[6,3] |
$-\,2^{22}\cdot 23^{7}$ |
$2$ |
$22.1936924282$ |
$48.602826013129224$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$4845.58364777$ |
| 12.0.15407021574586368.11 |
$x^{12} - 6 x^{10} + 27 x^{8} - 128 x^{6} + 336 x^{4} - 384 x^{2} + 192$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{15}$ |
$2$ |
$22.3345166185$ |
$44.62120719642371$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$15272.5110389$ |
| 12.0.15407021574586368.12 |
$x^{12} - 6 x^{10} - 12 x^{9} + 3 x^{8} + 108 x^{7} + 24 x^{6} - 216 x^{5} - 30 x^{4} - 176 x^{3} + 384 x^{2} + 192$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{15}$ |
$2$ |
$22.3345166185$ |
$44.62120719642371$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[3]$ |
$2$ |
$5$ |
$6993.69452827$ |
| 12.6.16515022032478208.1 |
$x^{12} - 5 x^{11} - x^{10} + 26 x^{9} + 12 x^{8} - 48 x^{7} - 105 x^{6} - 39 x^{5} + 73 x^{4} + 66 x^{3} + 50 x^{2} + 48 x + 16$ |
$12$ |
[6,3] |
$-\,2^{13}\cdot 17^{10}$ |
$2$ |
$22.4641468658$ |
$37.780041142444276$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$27038.3788257$ |
| 12.0.37913186137014272.1 |
$x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{6} + 25 x^{4} - 12 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{27}\cdot 7^{10}$ |
$2$ |
$24.0749756711$ |
$34.04715710793443$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[6]$ |
$2$ |
$5$ |
$3327.43294702$ |
| 12.6.41085390865563648.2 |
$x^{12} - 12 x^{10} - 8 x^{9} + 90 x^{8} + 24 x^{7} - 296 x^{6} - 72 x^{5} + 267 x^{4} - 48 x^{3} - 72 x^{2} + 72 x - 18$ |
$12$ |
[6,3] |
$-\,2^{33}\cdot 3^{14}$ |
$2$ |
$24.2367259333$ |
$24.23672593327708$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$68022.0886135$ |
| 12.6.41085390865563648.3 |
$x^{12} - 12 x^{10} - 16 x^{9} - 18 x^{8} - 72 x^{7} - 100 x^{6} - 48 x^{5} + 39 x^{4} + 112 x^{3} + 84 x^{2} + 24 x - 2$ |
$12$ |
[6,3] |
$-\,2^{33}\cdot 3^{14}$ |
$2$ |
$24.2367259333$ |
$36.79242356556043$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$42645.3812934$ |
| 12.0.41085390865563648.18 |
$x^{12} - 12 x^{10} + 18 x^{8} + 108 x^{6} + 153 x^{4} + 144 x^{2} + 72$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{14}$ |
$2$ |
$24.2367259333$ |
$36.79242356556043$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[2]$ |
$2$ |
$5$ |
$15480.7176618$ |
| 12.0.41085390865563648.22 |
$x^{12} - 4 x^{11} + 10 x^{10} - 28 x^{9} + 91 x^{8} - 208 x^{7} + 460 x^{6} - 784 x^{5} + 1090 x^{4} - 1152 x^{3} + 888 x^{2} - 576 x + 216$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{14}$ |
$2$ |
$24.2367259333$ |
$59.95318879120351$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[2]$ |
$2$ |
$5$ |
$24461.4495528$ |
| 12.6.46221064723759104.1 |
$x^{12} - 12 x^{10} + 18 x^{8} + 100 x^{6} - 351 x^{4} + 1224 x^{2} - 784$ |
$12$ |
[6,3] |
$-\,2^{30}\cdot 3^{16}$ |
$2$ |
$24.4757868319$ |
$47.429446013156884$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$40515.3160426$ |
| 12.6.51998697814228992.5 |
$x^{12} - 12 x^{10} - 4 x^{9} + 54 x^{8} + 36 x^{7} - 104 x^{6} - 108 x^{5} + 57 x^{4} + 132 x^{3} + 36 x^{2} - 72 x - 12$ |
$12$ |
[6,3] |
$-\,2^{27}\cdot 3^{18}$ |
$2$ |
$24.7172057269$ |
$44.62120719642371$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$76259.2364895$ |
| 12.6.51998697814228992.22 |
$x^{12} - 12 x^{10} - 12 x^{9} + 54 x^{8} + 108 x^{7} - 40 x^{6} - 324 x^{5} - 327 x^{4} + 204 x^{3} + 612 x^{2} + 360 x + 52$ |
$12$ |
[6,3] |
$-\,2^{27}\cdot 3^{18}$ |
$2$ |
$24.7172057269$ |
$44.62120719642371$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$52400.898619$ |
| 12.6.175495605123022848.1 |
$x^{12} - 12 x^{10} + 54 x^{8} - 60 x^{6} - 207 x^{4} + 432 x^{2} - 192$ |
$12$ |
[6,3] |
$-\,2^{24}\cdot 3^{21}$ |
$2$ |
$27.3540846835$ |
$39.4514168808688$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$114275.726808$ |
| 12.0.339365979862212608.1 |
$x^{12} - 3 x^{11} - 14 x^{10} + 39 x^{9} + 87 x^{8} - 190 x^{7} - 197 x^{6} + 219 x^{5} - 342 x^{4} + 769 x^{3} + 2099 x^{2} - 318 x + 18$ |
$12$ |
[0,6] |
$2^{13}\cdot 23^{10}$ |
$2$ |
$28.899413252$ |
$48.602826013129224$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[3]$ |
$2$ |
$5$ |
$23317.3801479$ |
| 12.6.369768517790072832.1 |
$x^{12} - 12 x^{10} + 54 x^{8} - 44 x^{6} - 303 x^{4} + 576 x^{2} - 128$ |
$12$ |
[6,3] |
$-\,2^{33}\cdot 3^{16}$ |
$2$ |
$29.1067798457$ |
$56.40343465948361$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$129054.84646$ |
| 12.0.369...832.84 |
$x^{12} - 12 x^{10} - 8 x^{9} + 54 x^{8} + 72 x^{7} + 96 x^{6} - 216 x^{5} - 1143 x^{4} + 1304 x^{3} + 1836 x^{2} - 3264 x + 1388$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{16}$ |
$2$ |
$29.1067798457$ |
$56.40343465948361$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
$[3]$ |
$2$ |
$5$ |
$28967.3708251$ |
| 12.0.497393604742873088.1 |
$x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 248 x^{8} - 398 x^{7} + 465 x^{6} - 398 x^{5} + 248 x^{4} - 110 x^{3} + 33 x^{2} - 6 x + 1$ |
$12$ |
[0,6] |
$2^{22}\cdot 17^{9}$ |
$2$ |
$29.8349295326$ |
$29.834929532638093$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
$[4]$ |
$2$ |
$5$ |
$4343.3187615$ |
| 12.0.124...808.24 |
$x^{12} - 12 x^{10} + 90 x^{8} - 332 x^{6} + 873 x^{4} - 216 x^{2} + 48$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{19}$ |
$2$ |
$32.211946996$ |
$72.71017779983123$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$83050.2557504$ |
| 12.0.124...808.36 |
$x^{12} - 8 x^{9} + 36 x^{8} + 96 x^{7} + 8 x^{6} - 432 x^{5} + 972 x^{4} + 288 x^{3} + 2160 x^{2} - 1152 x + 528$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{19}$ |
$2$ |
$32.211946996$ |
$72.71017779983123$ |
|
|
|
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$5$ |
$170326.394877$ |
